Termination of rewriting systems by polynomial interpretations and its implementation
Science of Computer Programming
Journal of Symbolic Computation
Termination proofs and the length of derivations
RTA-89 Proceedings of the 3rd international conference on Rewriting Techniques and Applications
Handbook of theoretical computer science (vol. B)
Termination proofs by multiset path orderings imply primitive recursive derivation lengths
Theoretical Computer Science - Selected papers of the Second International Conference on algebraic and logic programming, Nancy, France, October 1–3, 1990
Generating polynomial orderings
Information Processing Letters
Termination of term rewriting: interpretation and type elimination
Journal of Symbolic Computation - Special issue on conditional term rewriting systems
Term rewriting and all that
Proceedings of the 12th Conference on Foundations of Software Technology and Theoretical Computer Science
Incremental Termination Proofs and the Length of Derivations
RTA '91 Proceedings of the 4th International Conference on Rewriting Techniques and Applications
Polynomial Interpretations and the Complexity of Algorithms
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Generating Polynomial Orderings for Termination Proofs
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
An Early Program Proof by Alan Turing
IEEE Annals of the History of Computing
Proving Quadratic Derivational Complexities Using Context Dependent Interpretations
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Automated Complexity Analysis Based on the Dependency Pair Method
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Cdiprover3: a tool for proving derivational complexities of term rewriting systems
ESSLLI'08/09 Proceedings of the 2008 international conference on Interfaces: explorations in logic, language and computation
Revisiting matrix interpretations for polynomial derivational complexity of term rewriting
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Satisfiability of non-linear (Ir)rational arithmetic
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Derivational complexity of knuth-bendix orders revisited
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Complexity invariance of real interpretations
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
On the domain and dimension hierarchy of matrix interpretations
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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Proving termination of a rewrite system by an interpretation over the natural numbers directly implies an upper bound on the derivational complexity of the system. In this way, however, the derivation height of terms is often heavily overestimated. Here we present a generalization of termination proofs by interpretations that can avoid this drawback of the traditional approach. A number of simple examples illustrate how to achieve tight or even optimal bounds on the derivation height. The method is general enough to capture cases where simplification orderings fail.